Abstract
We consider the colored-noise-driven archetypal bistability dynamics of the Ginzburg-Landau type. The focus is on the stationary behavior and the problem of escape from metastable states. The deterministic flow of the underlyingtwo-variable Fokker-Planck process is studied as a function of the noise correlation time τ. As a main result we find that the separatrix exhibits a cusp at asymptotically large noise color. The stationary probability is evaluated approximately (unified colored noise approximation) and compared with numerical exact results. The stationary probability forms the key input in the evaluation of the rate of escape. At very strong noise color, the escape path closely follows a nodal line, passing through the corresponding stable node. The asymptotic result for the escape rate at large τ is compared with exact calculations for the lowest, nonvanishing eigenvalue.
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Hänggi, P., Jung, P. & Marchesoni, F. Escape driven by strongly correlated noise. J Stat Phys 54, 1367–1380 (1989). https://doi.org/10.1007/BF01044720
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DOI: https://doi.org/10.1007/BF01044720